Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches

14521 12 76950 2 212694 document 76950 Hanel_2017_New_J._Phys._19_033008.pdf application/pdf 65c02fafeef28c48f99676068e5e293b MD5 1146586 2017-04-05 07:01:53 https://pure.iiasa.ac.at/id/eprint/14521/1/Hanel_2017_New_J._Phys._19_033008.pdf 14521 1 1 application/pdf text en public cc_by

Hanel_2017_New_J._Phys._19_033008.pdf

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/76950 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/76950 http://eprints.org/relation/issmallThumbnailVersionOf https://pure.iiasa.ac.at/id/document/76950 archive 353 disk0/00/01/45/21 2017-04-05 07:04:52 2021-08-27 17:41:50 2017-04-05 07:04:52 article show Hanel R. Corominas-Murtra B. Thurner S. 1918 Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches pub prog_asa Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent processes. Their statistics is typically non-multinomial in the sense that the multiplicities of the occurrence of states is not a multinomial factor. The maximum entropy principle is tightly related to multinomial processes, non-interacting systems, and to the ensemble picture; it loses its meaning for path-dependent processes. Here we show that an equivalent to the ensemble picture exists for path-dependent processes, such that the non-multinomial statistics of the underlying dynamical process, by construction, is captured correctly in a functional that plays the role of a relative entropy. We demonstrate this for self-reinforcing Pólya urn processes, which explicitly generalize multinomial statistics. We demonstrate the adequacy of this constructive approach towards non-multinomial entropies by computing frequency and rank distributions of Pólya urn processes. We show how microscopic update rules of a path-dependent process allow us to explicitly construct a non-multinomial entropy functional, that, when maximized, predicts the time-dependent distribution function. 2017-03-06 published IOP 10.1088/1367-2630/aa611d 307 public New Journal of Physics 19 3 e033008 TRUE 1367-2630 multi-LAyer SpAtiotemporal Generalized NEtworks (LASAGNE, FP7 318132) Foundational Research on MULTIlevel comPLEX networks and systems (MULTIPLEX, FP7 317532) FALSE yes info:eu-repo/grantAgreement/EC/FP7/318132/EU//LASAGNE; info:eu-repo/grantAgreement/EC/FP7/317532/EU//MULTIPLEX info:eu-repo/semantics/article info:eu-repo/semantics/openAccess